Abstract
We make the notion of scope in the λ-calculus explicit. To that end, the syntax of the λ-calculus is extended with an end-of-scope operator ⋌, matching the usual opening of a scope due to λ. Accordingly, β-reduction is extended to the set of scoped λ-terms by performing minimal scope extrusion before performing replication as usual. We show confluence of the resulting scoped β-reduction. Confluence of β-reduction for the ordinary λ-calculus is obtained as a corollary, by extruding scopes maximally before forgetting them altogether. Only in this final forgetful step, α-equivalence is needed. All our proofs have been verified in Coq.
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Hendriks, D., van Oostrom, V. (2003). ⋌. In: Baader, F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science(), vol 2741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45085-6_11
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DOI: https://doi.org/10.1007/978-3-540-45085-6_11
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